Applying CAPM When Risk-Free and Market Returns Are Negative

Summary

The discussion explains how negative inputs affect the Capital Asset Pricing Model (CAPM), which estimates an asset’s expected return from the risk-free rate and its beta-adjusted market risk premium. The formula still applies when rates are negative: the premium is the market return minus the risk-free rate, and beta scales that difference before it is added to the risk-free rate.

The example uses a negative risk-free rate and an even lower market return. One answer points out that this conflicts with the CAPM equilibrium assumption that the market return exceeds the risk-free return; investors would not ordinarily choose risky assets expected to underperform the risk-free alternative. Another answer illustrates the arithmetic and explains that a negative risk-free rate changes the resulting expected return. The exchange offers a conceptual explanation and a numerical illustration, not empirical evidence. Its result depends on the stated inputs and on CAPM assumptions, so it does not establish that the model is reliable for forecasting in any particular market.

Key ideas

• CAPM uses the risk-free rate plus beta times the market risk premium.
• The market risk premium is the market return minus the risk-free rate, including when rates are negative.
• The discussion treats a market return below the risk-free rate as inconsistent with CAPM equilibrium.
• The example illustrates formula arithmetic rather than evidence that CAPM predicts realized returns.

Tags

# how negative rates (mr and rf) affect CAPM


# how negative rates (mr and rf) affect CAPM












I don't understand how the negative rates factor into this and what it means in the market

```
Beta= .73
rf= (-) 0.0032  
mr= (-)0.0264

CAPM =  [(-)0.0032 + [(-) 0.0264 – (-) 0.0032]0.73 = ???
```

## Answer by nbbo2 (score 2)

https://quant.stackexchange.com/a/21001

Although Rf can be negative (but not too negative), Rm cannot be less than Rf as in your example. It is a non-equilibrium situation, no one would invest in risky securities if they have an expectation lower than risk-free securities. So Rm > Rf is a necessary assumption of the CAPM, whether rates are positive or negative. Also, algebra is algebra and the CAPM is the CAPM, there is no CAPM2.

## Answer by Rime (score 0)

https://quant.stackexchange.com/a/21000

The risk free rate can be viewed as the opportunity cost to hold an investment i.e. Every risky investment should at least pay out the risk free rate. This is why you subtract the Rf from the Rm

When yields are negative you would have to add the Rf to Rm meaning you should expect to earn a much lower return [everything else held constant]:

```
CAPM1= negative interest rates
CAPM2= positive interest rates

Beta= .73
rf= (-) 0.0032  
mr= (-)0.0264

CAPM1=  [(-)0.0032 + [(-) 0.0264 – (-) 0.0032]0.73 = -2.0136%

CAPM2=  [0.0032 + [(-) 0.0264 – 0.0032]0.73 = -1.8408%
```

Remember that CAPM is the expected return on the investment

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